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IBDP Physics- A.2 Forces and momentum- IB Style Questions For SL Paper 2 -FA 2025

IBDP Physics SL Paper 1 -FA 2025- All Chapters

Question

The diagram shows an arrangement used to test golf club heads.
Golf club head test arrangement
The shaft of a club is pivoted and the centre of mass of the club head is raised by a height \(h\) before being released. On reaching the vertical position, the club head strikes the ball.
(a)
(i) Describe the energy changes that take place in the club head from the instant the club is released until the club head and the ball separate.
(ii) Calculate the maximum speed of the club head achievable when \(h = 0.85\,\text{m}\). [4]
(b) The diagram shows the deformation of a golf ball and club head as they collide during a test.
Golf ball deformation
Explain how increasing the deformation of the club head may be expected to increase the speed at which the ball leaves the club. [2]

(c)
In a different experimental arrangement, the club head is in contact with the ball for a time of \(220\,\mu\text{s}\). The club head has mass \(0.17\,\text{kg}\) and the ball has mass \(0.045\,\text{kg}\). At the moment of contact, the ball is at rest and the club head is moving with speed \(38\,\text{m}\,\text{s}^{-1}\). The ball moves off with an initial speed of \(63\,\text{m}\,\text{s}^{-1}\).

(i) Calculate the average force acting on the ball while the club head is in contact with the ball.
(ii) State the average force acting on the club head while it is in contact with the ball.
(iii) Calculate the speed of the club head at the instant that it loses contact with the ball. [5]

Most-appropriate topic codes (IB Physics):

• Topic A.2: Forces and momentum — parts (a), (b) and (c)
▶️ Answer/Explanation
Detailed solution

(a)
(i) Gravitational potential energy of the club head is converted into kinetic energy. During the collision, some kinetic energy is transferred to the ball and some becomes internal energy due to deformation.
(ii) Using energy conservation:
\(mgh = \tfrac{1}{2}mv^2 \Rightarrow v = \sqrt{2gh} \approx 4.1\,\text{m}\,\text{s}^{-1}\).

(b)
Increased deformation increases the contact time. A longer contact time produces a greater impulse, resulting in a larger change in momentum and hence a higher speed of the ball.

(c)
(i) Average force \(F = \dfrac{\Delta p}{\Delta t} \approx 1.3 \times 10^{4}\,\text{N}\).
(ii) The force on the club head is equal in magnitude and opposite in direction (Newton’s third law).
(iii) Using conservation of momentum, the speed of the club head after contact is approximately \(21\,\text{m}\,\text{s}^{-1}\).

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